A “bean counter” (or “bean-counter”) is an accountant or someone else who checks numbers (usually financial numbers), as if that person is counting beans.  “Bean-counter” has been cited in print since at least 1969 and possibly originated in the Pentagon. The term “bean counter” was in use in the auto industry by at least 1971.
 
A similar term to “bean counter” is “number cruncher.”
 
   
Wiktionary: bean counter
Alternative forms
. bean-counter
Noun
bean counter (plural bean counters)
1.(idiomatic, mildly derogatory) A person, such as an accountant or financial officer, who is concerned with quantification, especially to the exclusion of other matters.
 
(Oxford English Dictionary)
bean-counter, n.
Forms:  Also bean counter, beancounter.
colloq. (orig. and chiefly U.S.).
An accountant, esp. one who compiles statistical records or accounts; also applied contempt. to financial planners or statisticians. Hence, a person excessively concerned with accounts or figures.
1975 Interfaces Feb. 74 (title)  The measure of M.S./O.R. applications; or, Let’s hear it for the bean counters.
1982 N.Y. Times Mag. 14 Nov. 86/2   Tension between engineers and marketing specialists..and financial experts, derided as ‘bean counters,’ are [sic] endemic in the automobile business.
       
14 March 1969, Delaware County (PA) Daily Times, “Annual Family Report?” by Worthal, pg. 15, col. 1:
“Also a reorganization of the financial section of the company took place, in which the company president replaced the chief cook and bottle washer, as keeper of the books and head bean-counter.”
 
Google Books
A Matter of Accountability:
The true story of the Pueblo affair
By Trevor Armbrister
London: Barrie & Jenkins
1970  
Pg. 88:
Then, in December, 1965, McNamara’s budget experts— known in the Pentagon as the “bean counters”— reduced it even further, to $8600000.
 
Google Books
The Big Buck and the New Business Breed
By E. A. Butler
New York, NY: Macmillan
1972  
Pg. 19:
One of Iacocca’s fellow executives, comparing him and McNamara, says: “McNamara’s a bean counter . . . Iacocca has shown he can not only count the beans, he can put pizzazz in too.”
 
24 December 1972, Salt Lake Tribune (Salt Lake City, UT), “Author blasts Detroit for mediocre models,” pg. 2E, col. 7:
“The Death of the Automobile,” by John Jerome, W. W. Norton & Co. $6.95.
The evils of Detroit’s auto makers are superbly noted in this book—especially those of the auto-company bean counters who go through elaborate contortions to save a few dimes on each car made at the expense of worthy features. 
 
Google Books
30 April 1975, Computerworld, “The Scheduling Game: A Play of Comedy and Tragedy” by Anthony Constable, pg. S/4, col. 3:
That was Bean Counter in Accounting complaining as usual about not having received the customer billing run on time.
 
19 April 1976, Christian Science Monitor, “Chrysler, much leaner now, comes up fighting” by Charles E. Dole, pg. 20:
Chrysler has long been attacked for being run by “bean counters”—financial men.
 
OCLC WorldCat record
Lives of famous accountants
Author: C Clifton Farnsworth
Publisher: [Minneapolis? Minn.] : Bean Counter Press, ©1985.
Edition/Format:  Book : Biography : English
 
OCLC WorldCat record
The federal bean counter : the entire U.S. government budget made simple
Author: Bean & Associates. Federal Finance Division.
Publisher: Newburyport, MA : Bean & Associates, 1992.
Edition/Format:  Book : English